This paper proposes a general framework to use the cross tensor approximation or tensor CUR approximation for reconstructing incomplete images and videos. The new algorithms are simple and easy to be implemented with low computational complexity. For the case of data tensors with 1) structural missing components or 2) a high missing rate, we propose an efficient smooth tensor CUR algorithms which first make the sampled fibers smooth and then apply the proposed CUR algorithms. The main contribution of this paper is to develop/investigate improved multistage CUR algorithms with filtering (smoothing ) preprocessing for tensor completion. The second contribution is a detailed comparison of the performance of image recovery for four different CUR strategies via extensive computer simulations. Our simulations clearly indicated that the proposed algorithms are much faster than most of the existing state-of-the-art algorithms developed for tensor completion, while performance is comparable and often even better. Furthermore, we will provide in GitHub developed software in MATLAB which can be used for various applications. Moreover, to our best knowledge, the CUR (cross approximation) algorithms have not been investigated nor compared till now for image and video completion.
翻译:本文建议了一个使用交叉光度近似值或强光度 CUR 近似值来重建不完整图像和视频的一般框架。 新的算法简单易行, 且计算复杂度低。 对于具有1个结构性缺失部件或2个缺失率高的数据分解器的情况, 我们建议一个高效的光滑高光度 CUR 算法, 首先使样本纤维平滑, 然后应用拟议的 CUR 算法。 本文的主要贡献是开发/ 投资平台上改进的多级 CUR 算法, 过滤( 移动) 预处理以完成 。 第二个贡献是通过广泛的计算机模拟对四种不同的 CUR 战略的图像恢复性能进行详细比较。 我们的模拟清楚地表明, 拟议的算法比大多数为 Exlor 完成而开发的现有状态的算法要快得多, 而性能可以比较, 并且往往更好。 此外, 我们将在 GitHub 中提供可用于各种应用的筛选( 移动) 预处理的多级 CUR 软件。 此外, 目前还没有对 CUR (交叉近距) 算法进行过调查, 也没有对图像和图像完成进行比较。